Syllabus
Lecture Notes
Time and Location
M-W-F Period 3 (9:35 AM – 10:25 AM), LIT 127
Office Hours
Monday 3:00 PM – 3:50 PM, Wednesday 3:00 PM – 3:50 PM, Friday 12:45pm – 1:30pm, or by appointment
Textbook
- Witold A. J. Kosmala, A friendly introduction to analysis, 2nd Edition
Final Exam Date
Thursday, May 2 (5/2/2019) at 3:00 PM – 5:00 PM in LIT 127
Scope of the course
Intended for students who have completed the calculus sequence and linear algebra, the course helps in the pursuit of career in sciences, statistics, engineering, computer science, Economics, and business. A large portion of the material covered should sound familiar to students from their study of elementary calculus (such as real numbers, sequences, functions, limits, continuity, differentiation and integration, etc). However, the emphasis of the course is on Theory and deeper understanding. Students will develop skills with Proofs, will learn to interrelate ideas, and will improve their ability to reason carefully and creatively when dealing with mathematical ideas. An important goal of the course is to be able to express mathematical ideas in precise terms and communicate them clearly.
Who Should Take This Course
The fundamental ideas of calculus play an important role in sciences and engineering. For this reason, students in these areas may choose to take this course, even though no particular applications are discussed in the course. Students in mathematics, education, and other areas may also choose to take this course. However, the course is Not Recommended for students who plan to pursue graduate studies in mathematics; these students should take MAA 4211 instead.
Prerequisite
MAC 2313 or MAC 3474, and MAS 4105 or MAS 3114
Topics Covered
We will cover much of Chapters 1 to 5 of the textbook. Topics include sequences, functions, limits, continuity and differentiation. Below is the tentative weekly schedule:
W1: Algebra of sets, Mathematical Induction, Proof Techniques.
W2: Ordered fields and the real number system.
W3: Some properties of real numbers.
W4: Convergence of sequences, finite limits, monotone sequences.
W5: Cauchy sequences, subsequences.
W6: Applications of limits, the transcendental number e.
W7: Limits of functions, sided limits.
W8: Continuity of a function, properties of continuous functions.
W9: Uniform continuity.
W10: Applications of continuity, compact sets.
W11: Derivatives of a function, properties of differentiable functions.
W12: Mean value theorems.
W13: Higher-order derivatives, L’Hopital’s rule.
W14: Approximation of derivatives, convex functions.
Process for online Exams:
On XXX at 9:35am, the midterm will be posted here (course website) and on Canvas.
You will have 50 minutes to complete the exam.
Then, you will need to scan or take a picture of your test, and send it to me via email at a.marsiglietti@ufl.edu (pdf or jpeg file).
The deadline to submit your test is 11:00am on XXX.
MAKE SURE YOUR FILE IS READABLE BEFORE SUBMISSION. Also, I will acknowledge receipt of your email. If you do not receive an acknowledgement from me by 11:15am, you need to contact me (and resend your file).
I trust that you will not seek external help.
Please keep in mind the Honor Code at the University of Florida, the following pledge is either required or implied:
“On my honor, I have neither given nor received unauthorized aid in doing this assignment.”